DISA

Welcome to the next talk related to Webinar DISA-DSM: stochastic analysis, statistics and machine learning, which is held by Huyên Pham (University Paris 7 Diderot, France)

When? 3 November at 13:00 Stockholm time.
Online via zoom: Contact Nacira Agram, nacira.agram@lnu.se, to get the link

Title: Solving mean-field PDE with symmetric neural networks
Abstract: We propose numerical methods for solving non-linear partial differential equations (PDEs) in the Wasserstein space of probability measures, which arise notably in the optimal control of McKean-Vlasov dynamics.
The method relies first on the approximation of the PDE in infinite dimension by a backward stochastic differential equation (BSDE) with a forward system of N interacting particles. We provide the rate of convergence of this finite-dimensional approximation for the solution to the PDE and its Lions-derivative. Next, by exploiting the symmetry of the particles system, we design a machine learning algorithm based on certain types of neural networks, named PointNet and DeepSet, for computing simultaneously the pair solution to the BSDE by backward induction through sequential minimization of loss functions. We illustrate the efficiency of the PointNet/DeepSet networks compared to classical feedforward ones, and provide some numerical results of our algorithm for the examples of a mean-field systemic risk and a mean-variance problem.
Based on joint work with M. Germain (LPSM, EDF) and X Warin (EDF).

We will book a room at LNU for those who wants to attend physically the seminar. Because of space restrictions due to Covid-19, please let me know if you want to do that.

A warm welcome!

Our new DISA-group Deterministic and Stochastic Modelling (DSM) invites you to a seminar on Tuesday 27th at 13.00, this seminar is a part of a seminar series so keep an eye out for more information.

Title: Rare events simulation: least-squares Monte Carlo method vs deep learning based shooting method

Speaker: Omar Kebiri (University B-TU Cottbus-Senftenberg, Germany)

Abstract: When computing small probabilities associated with rare events by Monte Carlo it so happens that the variance of the estimator is of the same order as the quantity of interest. Importance sampling is a means to reduce the variance of the Monte Carlo estimator by sampling from an alternative probability distribution under which the rare event is no longer rare. Determine the optimal (i.e. zero variance) changes of measure leads to a stochastic optimal control problem. The control problem can be solved by a stochastic approximation algorithm, using the Feynman-Kac representation of the associated dynamic programming equations which leads to an FBSDE, and we discuss numerical aspects for high-dimensional problems along with simple toy examples using two methods: least-squares Monte Carlo method and deep learning based shooting method.
Joint work with Carsten Hartmann, Lara Neureither, and Lorenz Richter.

Practical information: We will book a room at LNU for those who wants to attend physically the seminar. Because of space restrictions due to Covid-19, please let me know if you want to do that, otherwise a link will be provided. Contact Nacira Agram – nacira.agram@lnu.se for more information.